Dynamic properties of cyclic cosmologies

TL;DR

This paper investigates universal and model-independent properties of cyclic cosmologies, analyzing their dynamics and conditions for cyclic solutions across various modified gravity theories.

Contribution

It provides a systematic review of cyclic cosmologies, applies dynamic systems analysis, and explores conditions for cyclic solutions in modified gravity frameworks.

Findings

Identifies universal properties of cyclic models

Uses dynamic systems theorems to ensure cyclic solutions

Provides examples of cyclic cosmologies in modified gravity theories

Abstract

Our first goal in this work is to study general and model-independent properties of cyclic cosmologies. The large number of studies of bouncing cosmologies and different cyclic scenarios published recently calls for a proper understanding of the universal properties of cyclic models. We thus first review and further elaborate the common physical and geometrical properties of various classes of cyclic models and then discuss how cyclic Universe can be treated as a dynamic system. We then discuss how two theorems from dynamic systems analysis can be used to ensure the existence of cyclic cosmological solutions under certain conditions on the field equations. After this we proceed towards our second goal which is the application of the obtained results to different frameworks of modified gravity theories: $f(R)$ gravity, dynamic dark energy and $f(T)$ gravity. We discuss the general requirements for the existence of cyclic solutions in these theories and also obtain various examples of cyclic cosmologies, while discussing their basic properties.